Assessing sensitivity in a multidimensional space: Some problems and a definition of a generald′

This article provides a formal definition for a sensivity measure,d′g, between two multivariate stimuli. In recent attempts to assess perceptual representations using qualitative tests on response probabilities, the concept of ad′ between two multidimensional stimuli has played a central role. For example, Kadlec and Townsend (1992a, 1992b) proposed several tests based on multidimensional signal detection theory that allow conclusions concerning the perceptual and/or decisional interactions of stimulus dimensions. One proposition, referred to as thediagonal d′test, relies on specific stimulus subsets of a feature-complete factorial identification task to infer perceptual separability. Also, Ashby and Townsend (1986), in a similar manner, attempted to relate perceptual independence to dimensional orthogonality in Tanner’s (1956) model, which also involvesd′ between two multivariate signals. An analysis of the proposedd′g reveals shortcomings in the diagonald′ test and also demonstrates that the assumptions behind equating perceptual independence to dimensional orthogonality are too weak. Thisd′g can be related to a common measure of statistical distance, Mahalanobis distance, in the special case of equal covariance matrices.